Q = 0
R = 0
r = 0 # remainder
- for i in range(15, -1, -1): # negative ranges are weird...
+ for i in range(64, -1, -1): # negative ranges are weird...
if (R>=0):
if (R<0):
R = R+((Q<<1)|1)
r = R
- return Q
+ return Q, r
# grabbed these from unit_test_single (convenience, this is just experimenting)
def main(mantissa, exponent):
if exponent & 1 != 0:
# shift mantissa up, subtract 1 from exp to compensate
- return sqrt(mantissa << 1), (exponent - 1) >> 1
- # mantissa as-is, no compensating needed on exp
- return sqrt(mantissa), (exponent >> 1)
+ mantissa <<= 1
+ exponent -= 1
+ m, r = sqrt(mantissa)
+ return m, r, exponent >> 1
+def fsqrt_test(x):
+
+ xbits = x.bits
+ print ("x", x, type(x))
+ sq_test = x.sqrt()
+ print ("sqrt", sq_test)
+
+ print (xbits, type(xbits))
+ s, e, m = decode_fp32(xbits)
+ print("x decode", s, e, m, hex(m))
+
+ m |= 1<<23 # set top bit (the missing "1" from mantissa)
+ m <<= 27
+
+ sm, sr, se = main(m, e)
+ lowbits = sm & 0x3
+ sm >>= 2
+ sm = get_mantissa(sm)
+ #sm += 2
+ print("our sqrt", s, se, sm, hex(sm), bin(sm), "lowbits", lowbits,
+ "rem", hex(sr))
+ if lowbits >= 2:
+ print ("probably needs rounding (+1 on mantissa)")
+
+ sq_xbits = sq_test.bits
+ s, e, m = decode_fp32(sq_xbits)
+ print ("sf32 sqrt", s, e, m, hex(m), bin(m))
+ print ()
+
if __name__ == '__main__':
# quick test up to 1000 of two sqrt functions
for Q in range(1, int(1e4)):
print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
- assert int(Q**0.5) == sqrt(Q), "Q sqrt fail %d" % Q
+ assert int(Q**0.5) == sqrt(Q)[0], "Q sqrt fail %d" % Q
# quick mantissa/exponent demo
for e in range(26):
for m in range(26):
- ms, es = main(m, e)
- print("m:%d e:%d sqrt: m:%d e:%d" % (m, e, ms, es))
+ ms, mr, es = main(m, e)
+ print("m:%d e:%d sqrt: m:%d-%d e:%d" % (m, e, ms, mr, es))
x = Float32(1234.123456789)
- xbits = x.bits
-
- print (x, type(x))
- print (xbits, type(xbits))
- s, e, m = decode_fp32(xbits)
- print(s, e, m, hex(m))
+ fsqrt_test(x)
+ x = Float32(32.1)
+ fsqrt_test(x)
+ x = Float32(16.0)
+ fsqrt_test(x)
+ x = Float32(8.0)
+ fsqrt_test(x)
+ x = Float32(8.5)
+ fsqrt_test(x)
+ x = Float32(3.14159265358979323)
+ fsqrt_test(x)
+ x = Float32(12.99392923123123)
+ fsqrt_test(x)
+ x = Float32(0.123456)
+ fsqrt_test(x)
- sq_test = x.sqrt()
- e, m = decode_fp32(sq_test)
- print(main(e, m))
"""
Notes: